Dynamic equations of an aircraft vehicle are derived under the assumption of a known and stationary Center of Gravity (CoG). Variations in loads result in a change in both of the aircraft vehicle's mass and the CoG position. The change in the CoG introduces undesirable couplings in flights dynamics. The variations in loads may be due to fuel consumption or change in payload of the aircraft vehicle. Knowledge of the CoG position is important for determination of the aircraft vehicle attitude, calculation of the various aerodynamics forces and torques, selection of the proper control strategy, and ensuring the aircraft vehicle stability.
An apparatus for tracking the center of gravity of an air vehicle was described in U.S. Pat. No. 8,260,477B2 entitled “METHOD AND APPARATUS FOR TRACKING CENTER OF GRAVITY OF AIR VEHICLE”, the entire disclosure of which is incorporated herein by reference. The apparatus estimates the angular velocity of the air vehicle from accelerometers measurements. The estimated vehicle angular velocity is then used to calculate both a center of gravity position and an inertial acceleration with respect to the vehicle's body frame using a suitable identification technique for a linear-in-parameters system. The estimation of the angular velocity may suffer from instability due to unstable nonlinear equations used. The accelerometers were arranged on rings. The rings are fitted into fore and aft positions of the air vehicles which impose some constraints on the airframe design.
A passive navigation system (PNS) was described in U.S. Pat. No. 6,014,103 entitled “PASSIVE NAVIGATION SYSTEM”, the entire disclosure of which is incorporated herein by reference. The PNS comprises an IMU that contains gyroscopes and accelerometers to provide the needed inertial information.
An autonomous covert Inertial Navigation System (INS) uniquely suited for underwater applications is described in U.S. Pat. No. 5,339,684 entitled “GRAVITY AIDED INERTIAL NAVIGATION SYSTEM”, the entire disclosure of which is incorporated herein by reference. The autonomous covert INS deals with errors correction where it ensures the Schuler and Sidereal errors are bounded. The autonomous covert INS utilizes a gradiometer, a gravimeter, and an inertial navigation system (INS) to facilitate its functionality. It can be used while navigating in varying gravity fields. However, the autonomous covert INS does not handle the Center of Gravity (CoG) shift.
A fault tolerant inertial reference system is described in U.S. Pat. No. 5,719,764 entitled “FAULT TOLERANT INERTIAL REFERENCE SYSTEM”, the entire disclosure of which is incorporated herein by reference. The fault tolerant inertial reference system employs two independent inertial reference units. Each unit utilizes global positioning system (GPS) information such as velocity and position. It also provides maximum level of fault tolerance with a minimum set of redundant inertial sensors where the faulty sensors can be isolated. It also provides means to correct the errors arising from the inertial sensors. However, it does not deal with the varying position of the CoG and varying gravity.
Therefore, there is a need for a method and system for determining the center of gravity position and the position rate of change under the influence of varying unknown gravitational force.
The foregoing “background” description is for the purpose of generally presenting the context of the disclosure. Work of the inventor, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present invention. The foregoing paragraphs have been provided by way of general introduction, and are not intended to limit the scope of the following claims. The described embodiments, together with further advantages, will be best understood by reference to the following detailed description taken in conjunction with the accompanying drawings.